Sinologists distinguish between the language as used in antiquity (Classical Chinese), and the language used after the fall of the Han Dynasty (Literary Chinese)
well, this description is slightly, . . . imprecise.
in joseph needlam’s book “science and civilization in china” volume vii, page 48:
When to use literary chinese in modern day?
depends on what do you mean “use” (reading, writing, or?)
the culture, history, nearly everything about chinese, before 1911, is recorded in literary chinese. so, to learn, comprehend these aspects, one must know how to read the texts in classical / literary chinese.
for writing, not many people can write literary chinese fluently nowadays, but, they tried hard. a recent example is, on 18 march 2020, an article “大流行緣起武漢” co-written by microbiologist yuen kwok-young, started in literary chinese; though not good, it’s impressive 😸
title & the first paragraph of the text:
full text is here
another usage is: terms used in correspondence (尺牘用語), these openings, endings, and greetings are strictly in literary chinese. again, not many can quote the terms correctly; those who can, would be treated as “high literacy”
about the character “係” (u+4fc2):
“係” used as “是”, this usage is quite old. i would say, the cantonese language preserved such usage, while others lost it.
in 平定準噶爾方略, it’s full of “係” used as “是”, such as: